scholarly journals A finite state projection algorithm for the stationary solution of the chemical master equation

2017 ◽  
Vol 147 (15) ◽  
pp. 154101 ◽  
Author(s):  
Ankit Gupta ◽  
Jan Mikelson ◽  
Mustafa Khammash
Keyword(s):  
Master Equation ◽  
Stationary Solution ◽  
Chemical Master Equation ◽  
Projection Algorithm ◽  
Finite State

scholarly journals A Parallel Implementation of the Finite State Projection Algorithm for the Solution of the Chemical Master Equation

2020 ◽  
Author(s):  
Huy Vo ◽  
Brian Munsky
Keyword(s):  
Master Equation ◽  
High Performance ◽  
Parallel Implementation ◽  
Chemical Species ◽  
Chemical Master Equation ◽  
Kolmogorov Equation ◽  
Projection Algorithm ◽  
Reaction Networks ◽  
Modeling Framework ◽  
Finite State

AbstractStochastic reaction networks are a popular modeling framework for biochemical processes that treat the molecular copy numbers within a single cell as a continuous time Markov chain, whose forward Chapman-Kolmogorov equation is known in biochemistry literature as the chemical master equation (CME). The solution of the CME contains extremely useful information that can be compared to experimental data in order to improve the quantitative understanding of biochemical reaction networks within the cell. However, this solution is costly to compute as it requires integrating an enormous system of differential equations that grows exponentially with the number of chemical species. To address this issue, we introduce a novel multiple-sinks Finite State Projection algorithm that approximates the CME with an adaptive sequence of reduced-order models with an effecient parallelization based on MPI. The implementation is tested on models of sizable state spaces using a high-performance computing node on Amazon Web Services, showing favorable scalability.

Modeling Stochastic Gene Regulatory Networks Using Direct Solutions of Chemical Master Equation and Rare Event Sampling

2016 ◽  
pp. 80-122
Author(s):  
Youfang Cao ◽  
Anna Terebus ◽  
Jie Liang
Keyword(s):  
Master Equation ◽  
Gene Regulatory Networks ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Rare Event ◽  
Planck Equation ◽  
Chemical Master Equation ◽  
Copy Numbers ◽  
Finite State ◽  
Gene Regulatory

Stochasticity plays important roles in many biological networks. A fundamental framework for studying the full stochasticity is the Discrete Chemical Master Equation (dCME). Under this framework, the combination of copy numbers of molecular species defines the microstate of the molecular interactions in the network. The probability distribution over these microstates provide a full description of the properties of a stochastic molecular network. However, it is challenging to solve a dCME. In this chapter, we will first discuss how to derive approximation methods including Fokker-Planck equation and the chemical Langevin equation from the dCME. We also discuss the widely used stochastic simulation method. After that, we focus on the direct solutions to the dCME. We first discuss the Finite State Projection (FSP) method, and then introduce the recently developed finite buffer method (fb-dCME) for directly solving both steady state and time-evolving probability landscape of dCME. We show the advantages of the fb-dCME method using two realistic gene regulatory networks.

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